← Emergence Series

Vortex Streets

An object in a flow creates alternating vortices that shed in a perfectly regular, metronomic pattern.

Hold a stick in a stream and swirls peel off alternately from each side, drifting downstream in a staggered zigzag. This is a von Kármán vortex street. Theodore von Kármán described it in 1911; satellite photos catch it behind ocean islands stretching for hundreds of kilometers.

A uniform flow hits a blunt obstacle, the boundary layers on each side become unstable, and one vortex growing on one side triggers the detachment of a vortex on the other. The frequency depends only on flow speed, obstacle size, and viscosity.

1. Flow Past a Cylinder

A Lattice Boltzmann simulation computes flow around a circular obstacle. At low speeds the flow wraps smoothly around the cylinder; raise the speed and vortices shed alternately from top and bottom.

Color shows vorticity. Blue is clockwise rotation, red is counterclockwise. The alternating downstream blobs are the vortex street.

0.06
Re: --
Regime: --

Figure 1. Lattice Boltzmann simulation of flow past a cylinder. Red and blue show the alternating spin of shed vortices. Increase the speed to trigger the instability.

2. The Reynolds Number

Whether the flow is smooth or chaotic depends on a single dimensionless quantity: the Reynolds number $Re = \rho v L / \mu$, where $\rho$ is fluid density, $v$ is flow speed, $L$ is obstacle diameter, and $\mu$ is dynamic viscosity. It represents the ratio of inertial forces to viscous forces.

At low Re viscosity wins and flow is laminar. As Re rises, the boundary layer separates and curls into vortices. Between roughly Re = 50 and 300 the shedding is periodic — a clean vortex street. Beyond that the wake turns turbulent.

3.0 m/s
2.0 cm
$Re = \rho v L / \mu = $ 400 ($\rho = 1000 \text{ kg/m}^3, \mu = 0.001 \text{ Pa}\cdot\text{s}$ for water)
Creeping
Steady
Vortex street
Turbulent
Re = 1 10 50 300 105
Re < 10 (Creeping)
Re ~ 10-40 (Steady)
Re ~ 50-300 (Vortex street)
Re > 300 (Turbulent)

Figure 2. The Reynolds number determines the flow regime. Adjust velocity and size to move along the scale.

3. Obstacle Shape

Any blunt body sheds vortices. Shape changes wake width, shedding frequency, and how cleanly vortices detach. Engineers track shedding with the Strouhal number:

$$ St = \frac{f L}{v} $$

where $f$ is the shedding frequency, $L$ the obstacle width, $v$ the flow speed. For a cylinder, St stays close to 0.2 across a wide range of Reynolds numbers. The simulation below measures it in real time from vorticity oscillations behind the obstacle.

0.07
St: --
Shedding period: --

Figure 3. Different shapes produce distinct wake patterns. The shedding frequency is remarkably stable across scales and fluids.

The Tacoma Narrows Bridge collapsed in 1940 partly because wind-driven vortex shedding matched the bridge's natural frequency. Tall chimneys often have helical strakes wrapped around them to break up the regular shedding pattern and prevent destructive oscillation.